Abstract
This chapter presents methodological guidelines that allow engineers to reuse generic ontologies. This kind of ontologies represents notions generic across many fields, (is part of, temporal interval, etc.). The guidelines helps the developer (a) to identify the type of generic ontology to be reused, (b) to find out the axioms and definitions that should be reused and (c) to adapt and integrate the generic ontology selected in the domain ontology to be developed. For each task of the methodology, a set of heuristics with examples are presented. We hope that after reading this chapter, you would have acquired some basic ideas on how to take advantage of the great deal of well-founded explicit knowledge that formalizes generic notions such as time concepts and the part of relation.
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Notes
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We consider a module (d’Aquin M et al. 2007b) as a part of the ontology that defines the relevant set of terms for a particular purpose.
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An ontology statement (or triple) contains the following three components: subject, predicate, and object.
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The rest of the cases are presented in Suárez-Figueroa (2010).
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The term module has here the pragmatic sense equivalent to the d’Aquin’s reference cited in the Introduction.
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Annex: Mereology
Annex: Mereology
A mereology is a formal theory of parts and associated concepts (Borst 1997; Schneider 2003). We have said “a mereology” instead of “the mereology” because different assumptions can be taken into account in the formalization of parthood. Therefore, different mereologies can be proposed.
In the following paragraphs, we will show one of the mereologies presented by Varzi (2007).
Theory M. Most of the authors agree on the following core of axioms (named with A) and definitions (named with D) (Varzi 2007). Along these paragraphs, we use examples of territories to clarify the meaning of axioms and definitions. The mentions to administrative units really refer to their physical territories.
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A.1. Reflexivity. Every object of the universe of discourse is a part of itself. For instance, the EU is part of the EU.
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A.2. Antisymmetry. If an object x is a part of y, and y is a part of x, then x and y are the same object. For instance, if the territory T 1 is part of the territory T 2, then the only way so that T 2 is part of T 1 is being T 1 and T 2 the same territory.
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A.3. Transitivity. If x is a part of y, and y is a part of z, then x is a part of z. For instance, the Community of Madrid is part of Spain, and Spain is part of the EU; therefore, the Community of Madrid is a part of the EU.
A number of additional mereological predicates can be then introduced by definition:
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D.1. Proper part. A proper part is a part that is other that the individual itself. For example, Spain is proper part of the EU, since Spain is part of the EU and they are different entities.
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D.2. Direct part. X is direct part of y if and only if x is proper part of y and there is no part between x and y Footnote 16. For example, Spain is direct part of the EU, but Madrid is not, since Spain is a part between Madrid and the EU.
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D.3. Overlap. The relation overlaps is defined as a sharing part. That is, x and y overlap if and only if there is a z such that z is part of x and part of y. For instance, Nordic countries and the EU overlap, since there are Nordic countries which are parts of the EU.
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D.4. Underlap. The relation underlaps is defined as a sharing whole. That is, x and y underlap if and only if there is a z such that x and y are parts of z. For example, the Netherlands, Sweden, and Spain underlap the same common whole: the EU.
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D.5. Disjoint. The disjoint relation is the logical negation of overlaps. For example, Belgium and the Netherlands are disjoint territories.
Theory M may be viewed as embodying the common core of any mereological theory. A.1–A.3 should be extended to build a mereology.
Minimal mereology (MM). A way to extend M is assuming the following principle (Varzi 2007):
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A.4. Weak supplementation principle. Every object x with a proper part y has another part z that is disjoint from y. The domain of territories, for example, fulfills this principle. For example, given that Spain is proper part of the EU, then the EU has other parts that are disjoint from Spain: the Netherlands, Luxemburg, Sweden, etc.
Most of the authors strengthen that A.4 should be incorporated to M as a further fundamental principle on the meaning of part of. Other authors provide scenarios that could be counterexamples of this principle. However, it is far from being demonstrated that such supposed counterexamples have implications in computer applications.
The rest of mereologies starting from MM are explained with examples in (Fernández López et al. 2008; Suárez-Figueroa 2010).
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Fernández-López, M., Suárez-Figueroa, M.C., Gómez-Pérez, A. (2012). Ontology Development by Reuse. In: Suárez-Figueroa, M., Gómez-Pérez, A., Motta, E., Gangemi, A. (eds) Ontology Engineering in a Networked World. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24794-1_7
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